To find local extrema in mathematics, you need to first find the critical points of the function by taking the derivative and setting it equal to zero. Then, you can use the second derivative test to determine whether each critical point is a local maximum, local minimum, or neither. If the second derivative is positive at a critical point, it is a local minimum, and if it is negative, it is a local maximum. **

In mathematics, a local minimum is a point on a graph where the function reaches its lowest value within a small neighborhood of that point. This means that the function has a lower value at that point than at any nearby points. A local minimum can occur at a relative low point on the graph, but it may not be the absolute lowest point on the entire graph. It is important to distinguish between local and global minimums when analyzing the behavior of a function. **

Thomas Hobbes' concept of human nature is that humans are inherently self-interested and driven by a desire for power and self-preservation. He believed that in a state of nature, without a governing authority, humans would be in a constant state of conflict and competition. Hobbes argued that to avoid this chaotic state, individuals would enter into a social contract and create a sovereign authority to maintain order and prevent the "war of all against all." **

Thomas Hobbes was largely self-taught and did not have a formal university education. He was well-read in classics, history, and philosophy. Jean-Jacques Rousseau, on the other hand, received a formal education and attended a seminary school. He later studied music and philosophy, which greatly influenced his ideas on education and society. **

The main difference between Hobbes and Rousseau lies in their views on human nature and the role of the state. Hobbes believed that humans are inherently selfish and competitive, and therefore require a strong central authority to maintain order and prevent chaos. In contrast, Rousseau believed that humans are inherently good and cooperative, and that the state should exist to protect individual freedom and promote the common good. Additionally, Hobbes advocated for an absolute monarchy, while Rousseau favored a more democratic form of government based on the general will of the people. **

The quote by Thomas Hobbes, "The condition of man... is a condition of war of everyone against everyone," reflects his belief in the inherently competitive and conflict-driven nature of human beings. Hobbes argued that in the absence of a strong central authority, individuals would constantly be in conflict with one another, leading to a state of perpetual war. This quote is often interpreted as a commentary on the need for a powerful government to maintain order and prevent chaos. Overall, the quote captures Hobbes' pessimistic view of human nature and his emphasis on the importance of a strong social contract to prevent societal breakdown. **

One of Hobbes' famous quotes about ethics is "the life of man, solitary, poor, nasty, brutish, and short." This quote reflects Hobbes' belief that without a strong central authority to enforce moral and ethical behavior, human life would be characterized by chaos and conflict. It emphasizes the importance of social order and the role of government in maintaining ethical standards within society. **

To find local extrema in mathematics, one must first find the critical points of the function by taking the derivative and setting it equal to zero. Then, one can use the second derivative test to determine whether each critical point corresponds to a local maximum, local minimum, or neither. If the second derivative is positive at a critical point, it is a local minimum, and if it is negative, it is a local maximum. **